Multiple-input Multiple-output Precoding Research Articles

A Poisson Shot Noise Limited MMSE Precoding for Photon-Counting MIMO Systems with Reinforcement Learning

With the development of the Internet of Things (IoT), most communication systems are difficult to implement on a large scale due to their high complexity. Multiple-input multiple-output (MIMO) precoding is a generally used technique for improving the reliability of free-space optical (FSO) communications, which is a key technology in the 6G era. However, traditional MIMO precoding schemes are typically designed based on the assumption of additive white Gaussian noise (AWGN). In this paper, we present a novel MIMO precoding method based on reinforcement learning (RL) that is specifically designed for the Poisson shot noise model. Unlike traditional MIMO precoding schemes, our proposed scheme takes into account the unique statistical characteristics of Poisson shot noise. Our approach achieves significant performance gains compared to existing MIMO precoding schemes. The proposed scheme can achieve the bit error rate (BER) of 10−5 in a strong turbulence channel and exhibits superior robustness against imperfect channel state information (CSI).

Deep Contextual Bandit and Reinforcement Learning for IRS-Assisted MU-MIMO Systems

The combination of multiple-input multiple-output (MIMO) systems and intelligent reflecting surfaces (IRSs) is foreseen as a critical enabler of beyond 5G (B5G) and 6G. In this work, two different approaches are considered for the joint optimization of the IRS phase-shift matrix and MIMO precoders of an IRS-assisted multi-stream (MS) multi-user MIMO (MU-MIMO) system. Both approaches aim to maximize the system sum-rate for every channel realization. The first proposed solution is a novel contextual bandit (CB) framework with continuous state and action spaces called deep contextual bandit-oriented deep deterministic policy gradient (DCB-DDPG). The second is an innovative deep reinforcement learning (DRL) formulation where the states, actions, and rewards are selected such that the Markov decision process (MDP) property of reinforcement learning (RL) is appropriately met. Both proposals perform remarkably better than state-of-the-art heuristic methods in scenarios with high multi-user interference.

SLNR-Based Beamspace Precoding and Beam Selection for Wideband mmWave Massive MIMO

Beamspace multiple-input multiple-output (MIMO) systems leverage the lens antenna array to reduce their hardware cost, which is a promising technology in millimeter wave (mmWave) frequency bands. This letter proposes a novel signal-to-leakage-plus-noise ratio (SLNR)-based beamspace precoding and beam selection scheme to improve the downlink sum rate (SR) of the beamspace mmWave massive MIMO channels. First, for a given beam subset, a SLNR maximization-based beamspace precoder is designed to mitigate the inter-user interference caused by leakage power, thus enhancing the SR. Then, an approximated expression of the SR is formulated, based on which an iterative radio frequency (RF) precoding and beam selection method is designed to further improve the system SR. Numerical results demonstrate a superior SR performance of the proposed scheme over state-of-the-art methods.

Robust Decentralized and Distributed Estimation of a Correlated Parameter Vector in MIMO-OFDM Wireless Sensor Networks

An optimal precoder design is conceived for the decentralized estimation of an unknown spatially as well as temporally correlated parameter vector in a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) based wireless sensor network (WSN). Furthermore, exploiting the temporal correlation present in the parameter vector, a rate-distortion theory based framework is developed for the optimal quantization of the sensor observations so that the resultant distortion is minimized for a given bit-budget. Subsequently, optimal precoders are also developed that minimize the sum-MSE (SMSE) for the scenario of transmitting quantized observations. In order to reduce the computational complexity of the decentralized framework, distributed precoder design algorithms are also developed which design precoders using the consensus based alternating direction method of multipliers (ADMM), wherein each SN determines its precoders without any central coordination by the fusion center. Finally, new robust MIMO precoder designs are proposed for practical scenarios operating in the face of channel state information (CSI) uncertainty. Our simulation results demonstrate the improved performance of the proposed schemes and corroborate our analytical formulations.

Antenna Clustering for Simultaneous Wireless Information and Power Transfer in a MIMO Full-Duplex System: A Deep Reinforcement Learning-Based Design

We propose a novel antenna clustering-based method for simultaneous wireless information and power transfer (SWIPT) in a multiple-input multiple-output (MIMO) full-duplex (FD) system. For a point-to-point communication set up, the proposed method enables a wireless device with multiple antennas to simultaneously transmit information and harvest energy using the same time-frequency resources. And the energy transmitting device with multiple antennas simultaneously receives information from the energy harvesting (EH) device. This is achieved by clustering the antennas into two MIMO subsystems: one for information transmission (IT) and another for EH. Furthermore, the self-interference (SI) signal at the EH device caused by the FD mode of operation is harvested by the device. For implementation-friendly antenna clustering and MIMO precoding, we propose two methods: (i) a sub-optimal method based on relaxation of objective function in a combinatorial optimization problem, and (ii) a hybrid deep reinforcement learning (DRL)-based method. For the proposed DRL solution, we design a hybrid discrete/continuous action agent that jointly clusters the MIMO antennas between EH and IT, and at the same time, find the best values for MIMO precoding matrices at both devices. This is achieved by using two interacting agent learning subsystems, namely, deep double Q-learning (DDQN), for antenna clustering and deep deterministic policy gradient (DDPG), for MIMO precoding. The effect of imperfect CSI is also studied and investigated. Finally, we study the performances of the two implementation methods and compare them with the conventional time switching-based simultaneous wireless information and power transfer (SWIPT) technique. Our findings show that the proposed MIMO clustering-based SWIPT method gives a significant improvement in spectral efficiency compared to the time switching-based SWIPT method. In particular, the DRL-based method provides the highest spectral efficiency. Besides, the numerical results show that, for the considered system set up, the number of antennas in each device should exceed three to mitigate self-interference to an acceptable level.

Local Partial Zero-Forcing Precoding for Cell-Free Massive MIMO

Cell-free Massive MIMO (multiple-input multiple-output) is a promising distributed network architecture for 5G-and-beyond systems. It guarantees ubiquitous coverage at high spectral efficiency (SE) by leveraging signal co-processing at multiple access points (APs), aggressive spatial user multiplexing and extraordinary macro-diversity gain. In this study, we propose two distributed precoding schemes, referred to as \textit{local partial zero-forcing} (PZF) and \textit{local protective partial zero-forcing} (PPZF), that further improve the spectral efficiency by providing an adaptable trade-off between interference cancelation and boosting of the desired signal, with no additional front-hauling overhead, and implementable by APs with very few antennas. We derive closed-form expressions for the achievable SE under the assumption of independent Rayleigh fading channel, channel estimation error and pilot contamination. PZF and PPZF can substantially outperform maximum ratio transmission and zero-forcing, and their performance is comparable to that achieved by regularized zero-forcing (RZF), which is a benchmark in the downlink. Importantly, these closed-form expressions can be employed to devise optimal (long-term) power control strategies that are also suitable for RZF, whose closed-form expression for the SE is not available.

Joint Modulation and Beamforming for MIMO Systems With 1-b DACs

To realize multiple-input multiple-output (MIMO) with low cost and low power consumption, the use of low-resolution digital-to-analog converters (DAC) is drawing significant interest. While previous studies on low-resolution DAC MIMO have focused on optimizing precoding for massive MIMO, this approach faces the limitation that the coarse resolution at the transmitter makes it difficult to construct a transmit signal close enough to the desired one when a small scale MIMO transmitter is considered as in IoT networks. To address this problem, we propose a new transmission framework that jointly performs modulation and beamforming. With the proposed scheme, a message symbol is directly mapped into a feasible transmit vector. We also develop a channel-adaptive mapping function within the proposed framework that minimizes error probability. Simulation results show that the proposed scheme can significantly improve the error performance.

Non-Linear and Non-Iterative Based Transceiver Design for SU-MIMO Systems

This paper considers the design of a low-complexity and high-performance precoder for multiple-input multiple-output (MIMO) systems. The precoder is designed by combining both nonlinear and non-iterative processing strategies. The proposed nonlinear precoding techniques employ a nonlinear constellation precoding technique based on maximum distance separable codes at the transmitter. We propose to reduce the computational complexity in iterative-based precoding algorithms by using less complex non-iterative singular value decomposition-based joint precoder and decoder pair design. The maximum likelihood detection for the linear MIMO channel is considered. The simulation results showed that the proposed nonlinear and non-iterative precoding schemes outperform the conventional linear MIMO precoder design, even when a reduced-complexity suboptimal strategy is adopted, considering the bit error rate performance.

Precoded MIMO Systems With Nonbinary LDPC Codes and Many-to-One Mapping

A precoding design is proposed for multiple-input multiple-output (MIMO) systems utilizing nonbinary low-density parity check (NB-LDPC) codes and many-to-one mapping. When a high-order modulation scheme is used, many-to-one mapping converts a group of low-order Galois field (GF) coded symbols into one modulated MIMO symbol vector. In contrast, one-to-one mapping maps a high-order modulation symbol directly from one high-order GF coded symbol. With the help of an interleaver between the NB-LDPC encoder and the GF to MIMO symbol mapper, the many-to-one mapping enables turbo receiver and reduces the computational complexity by more than 95%. The proposed MIMO precoders enhance the error-rate performance of the many-to-one NB-LDPC MIMO system, especially in terms of reducing the error floor and improving the waterfall region. The proposed precoder design modifies the approach that suboptimally maximizes the minimal Euclidean distance between the received MIMO symbols. Simulation results show that the proposed precoders enhance the robustness of the precoder design and reduce the inner and outer iterations of the turbo receiver.

Optimization of linear MIMO precoding assuming MMSE-based turbo equalization

In this paper, we focus on the optimization of a linear multiple-input multiple-output (MIMO) precoder assuming an outer forward error correction code and an iterative minimum mean square error (MMSE)-based interference cancellation (turbo equalization) at the receiver side. Given perfect channel state information at both sides of the communication, we propose a novel precoder that is specifically designed to use with turbo equalization. In contrast to the conventional precoders that maximize the mutual information (MI) between finite alphabet input and the corresponding output over the precoded MIMO channel, the proposed precoder aims to maximize the MI between the finite alphabet input and the corresponding output of the equalizer. The precoder is targeted for applications that require low complexity, where forward error correction (FEC) codes with low-complex encoding and decoding structures are used. Simulation results show the error-rate performance gain of the resulting precoder compared to two other reference precoders presented in the literature, which are derived from the maximization of the precoded MIMO channel MI.

Precoding for MIMO Channels in Cognitive Radio Networks with CSI Uncertainties and for MIMO Compound Capacity

Inaccurate knowledge of channel state information (CSI) limits the performance offered by multiple-input multiple-output (MIMO) communications. The design of a MIMO precoder needs to take the CSI uncertainty into consideration to mitigate its effects. This paper proposes a method to design the precoder for a secondary user in an underlay cognitive radio framework that maximizes its transmission performance, where the direct link to its receiver and the interference link to a primary user have CSI uncertainties. We model the CSI uncertainties through the Schatten norm that encompasses most commonly used norm measures such as the spectral and Frobenious norms. The proposed method solves iteratively a minimax problem by deriving the optimal solution for the worst case interference CSI uncertainty, applying the alternate-iterate technique for the worst case direct link CSI deviation, and developing a feasible direction projected subgradient technique for the precoder. Simpler solutions for the precoder are also derived under some specific norm measure of CSI uncertainty and certain requirement of transmission power. Simulations corroborate the expected performance of the proposed design.

Low-Complexity MIMO Precoding for Finite-Alphabet Signals

This paper investigates the design of precoders for single-user multiple-input multiple-output (MIMO) channels, and in particular for finite-alphabet signals. Based on an asymptotic expression for the mutual information of channels exhibiting line-of-sight components and rather general antenna correlations, precoding structures that decompose the general channel into a set of parallel subchannel pairs are proposed. Then, a low-complexity iterative algorithm is devised to maximize the sum mutual information of all pairs. The proposed algorithm significantly reduces the computational load of existing approaches with only minimal loss in performance. The complexity savings increase with the number of transmit antennas and with the cardinality of the signal alphabet, making it possible to support values thereof that were unmanageable with existing solutions. Most importantly, the proposed solution does not require instantaneous channel state information (CSI) at the transmitter, but only statistical CSI.

Performance of Open-Loop MIMO Precoder With Cross-Polarized Antennas Over Correlated Channels With an LOS Component

Open-loop multiple-input multiple-output (MIMO) precoders, that do not require channel information, were recently proposed to mitigate the performance degradation of spatial multiplexing (SM) due to spatial correlations and/or line-of-sight (LOS) component. The open-loop MIMO precoder technique has been adopted in next generation broadcasting systems, such as digital video broadcasting-next generation handheld (DVB-NGH) and advanced television systems committee (ATSC) 3.0 standards. Furthermore, in DVB-NGH and ATSC 3.0, cross-polarized antennas have been employed in order to overcome the insufficient antenna separation for co-polarized antennas, which can enhance the performance over high correlation and LOS conditions. In this paper, we analyze and evaluate the performance of the open-loop MIMO precoders with cross-polarized antennas over correlated channels with an LOS component. We first study the statistical property of the MIMO channel with cross-polarized antennas on the basis of the measurement-based channel model. Next, we derive pairwise error probability (PEP) of the SM with the open-loop MIMO precoder. Through the PEP derivation, we evaluate the performance of each open-loop MIMO precoder against the spatial correlations and LOS component with the effect of cross-polarized antennas. The simulation results are presented to demonstrate the performance of the open-loop MIMO precoders over various channel conditions.

Widely Linear Precoding for Large-Scale MIMO with IQI: Algorithms and Performance Analysis

In this paper, we study widely linear precoding techniques to mitigate in-phase/quadrature-phase (IQ) imbalance (IQI) in the downlink of large-scale multiple-input multiple-output (MIMO) systems. We adopt a real-valued signal model, which considers the IQI at the transmitter, and then develop widely linear zero-forcing (WL-ZF), widely linear matched filter, widely linear minimum mean-squared error, and widely linear block-diagonalization (WL-BD) type precoding algorithms for both single- and multiple-antenna users. We also present a performance analysis of WL-ZF and WL-BD. It is proved that without IQI, WL-ZF has exactly the same multiplexing gain and power offset as ZF, while when IQI exists, WL-ZF achieves the same multiplexing gain as ZF with ideal IQ branches, but with a minor power loss, which is related to the system scale and the IQ parameters. We also compare the performance of WL-BD with BD. The analysis shows that with ideal IQ branches, WL-BD has the same data rate as BD, while when IQI exists, WL-BD achieves the same multiplexing gain as BD without IQ imbalance. Numerical results verify the analysis and show that the proposed widely linear type precoding methods significantly outperform their conventional counterparts with IQI and approach those with ideal IQ branches.

MIMO Precoder Design With a Compensated QR-Decomposition Combination for CoMP Downlink Scenarios

This paper presents a multiple-input–multiple-output (MIMO) precoder with a compensated QR decomposition (CQRD) combination for coordinated multipoint (CoMP) downlink transmission. Unlike conventional QR decomposition (QRD) combination, CQRD combination adopts compensated channel matrix orderings. This paper first proposes CQRD combination for CoMP scenarios. The statistics for combined spatial subchannel gains with a CQRD combination of two coordinated base stations (BSs) are derived, and these statistics show that more balanced subchannel gains are generated with a CQRD combination than with a QRD combination. Furthermore, this paper proposes a generalized CQRD combination scheme with a joint sorting strategy that can be applied to scenarios with more than two coordinated BSs. Unlike the unsorted strategy, the joint sorting strategy determines an enhanced compensated combination to further increase spatial subchannel gains; therefore, the performance can be upgraded. Because conventional Tomlinson–Harashima precoding (THP) cannot be used in the CQRD combination, interference presubtraction and vector precoding (VP) is adopted. Theoretical analysis and simulation results are both provided to demonstrate the advantages of balanced spatial subchannel gains and enhanced bit-error-rate (BER) performance in the proposed CQRD-based schemes. Compared with existing QRD-based MIMO precoders in CoMP scenarios, the proposed CQRD-based schemes have substantial signal-to-noise ratio (SNR) improvements of 2–5 dB.

Hybrid precoding with compressive sensing based limited feedback in massive MIMO systems

ABSTRACTMassive multiple‐input multiple‐output (MIMO) systems are an enabling technology for high capacity 5G cellular networks. However, the high hardware complexity and power consumption make it difficult to apply conventional MIMO precoding schemes in massive MIMO. Additionally, thanks to the large channel dimension, applying traditional limited feedback schemes for obtaining channel state information at the transmitter is a challenge. In this paper, we develop a low‐complexity hybrid precoding scheme for multiuser massive MIMO system in mmWave communication. We design the analog beamformer as the conjugate transpose of the downlink channel from base station to the users. Then zero‐forcing baseband processing is applied over the effective channel. We get the optimal power allocation policy and compare its performance with average power allocation based on channel state information at transmitter. The channel state information at transmitter is obtained via a compressive sensing based limited feedback strategy. The effectiveness of hybrid precoding relies on the feedback quality of channel state information, which relies on the compression ratio. We quantify the impact of compression ratio on precoder performance and derive an upper bound on the sum rate. Simulation results illustrate the performance of our proposed scheme and the effect of compressive sensing based limited feedback.

MIMO Precoding for Correlated Fading Channels

This contribution proposes a precoder-decoder design aiming to improve the performance of multiple-input–multiple-output (MIMO) detectors under correlated fading channels. The MIMO detection principle namely minimum mean squared error (MMSE) detector is analyzed under such channel condition. The proposed approach deploys the channel state information (CSI) aiming to estimate the level of spatial correlation channel, namely normalized correlation index [Formula: see text] and uses this information to improve the MIMO system performance. Furthermore, the impact of the [Formula: see text] estimation errors on the performance, as well the performance degradation for different levels of correlation have been analyzed and compared with the classical MMSE-MIMO detector operating under uncorrelated channels and perfect channel estimation.

Codebook Size Design for RVQ-Based Tomlinson–Harashima Precoded MIMO Broadcast Channels

In this paper, we study the codebook size design strategies in the multiple-input–multiple-output (MIMO) broadcast channel (BC) systems. We adopt the nonlinear Tomlinson–Harashima precoder (THP), which is designed by the imperfect channel direction information (CDI) acquired from the random vector quantization (RVQ) feedback mechanism. Under the limitation of the total feedback rate, we flexibly allocate the size of each user's codebook so that the overall channel capacity is maximized. Since the design problem is not convex, directly finding out the optimum allocation of codebook size is not attainable. However, by sophisticatedly using the discrete majorization theory, we can derive the codebook size allocation strategies for the high- and the low-signal-to-noise-ratio (SNR) regions. Interestingly, the results show that the equal size codebook is preferable in the low-SNR region, whereas the codebook allocates the whole available codebook size to a single user in the high-SNR region. Simulations certify the theoretical result of our design.

Linear Precoding for MIMO With LDPC Coding and Reduced Complexity

In this paper, the problem of designing a linear precoder for Multiple-Input Multiple-Output (MIMO) systems employing Low-Density Parity-Check (LDPC) codes is addressed under the constraint of minimizing the dependence between the system's receiving branches, thus reducing the relevant transmitter and receiver complexities. Our approach constitutes an interesting generalization of Bit-Interleaved Coded Modulation with Multiple Beamforming (BICMB) which has shown many benefits in MIMO systems. We start with a Pareto optimal surface modeling of the system and show the difficulty involved in the corresponding optimization problem. We then propose an alternative, practical technique, called Per-Group Precoding (PGP), which groups together multiple input symbol streams and corresponding receiving branches in the “virtual” channel domain (after singular value decomposition of the original MIMO channel), and thus results in independent transmitting/receiving streams between groups. We show with numerical results that PGP offers almost optimal performance, albeit with significant reduction both in the precoder optimization and LDPC EXIT chart based decoding complexities.

Before/after precoding massive MIMO systems for cloud radio access networks

In this paper, we investigate two types of in-phase and quadrature-phase (IQ) data transfer methods for cloud multiple-input multiple-output (MIMO) network operation. They are termed “after-precoding” and “before-precoding”. We formulate a cloud massive MIMO operation problem that aims at selecting the best IQ data transfer method and transmission strategy (beamforming technique, the number of concurrently receiving users, the number of used antennas for transmission) to maximize the ergodic sum-rate under a limited capacity of the digital unit-radio unit link. Based on our proposed solution, the optimal numbers of users and antennas are simultaneously chosen. Numerical results confirm that the sum-rate gain is greater when adaptive “after/before-precoding” method is available than when only conventional “after-precoding” IQ-data transfer is available.